Classical solutions to the Fokker-Planck-BGK equation with infinite energy

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:437

Article

Chen, Zili¹ 

[1] Nanchang Univ, Sch Sci, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

关键词: Fokker-Planck-BGK equation;    Global existence;    Uniqueness;    Classical solution;    Infinite energy;   

DOI  :  10.1016/j.jmaa.2016.01.042

来源: Elsevier

【 摘 要 】

We consider the BGK equation perturbed by Fokker-Planck operator, which is important in the kinetic theory of rarefied gases. This model equation, which we call the Fokker-Planck-BGK equation, has many physical features that the Fokker-Planck-Boltzmann equation possesses. By establishing a new moments lemma and L-infinity bounds for macroscopic quantities without the boundedness of energy, we get several global existence and uniqueness results to the Cauchy problem of the Fokker-Planck-BGK equation under various circumstances with infinite energy. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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